Asparagus is actually among the list of foods that are acceptable to eat for people who have problems with migraine headaches. Some of the other foods that you can feel free to eat include spinach, green lettuce, broccoli, zucchini, squash, beets, corn, and string beans. All of these foods are extremely good for you and will not increase the risk of migraines whatsoever.
There are other foods which you will need to limit your intake of or cut out of your diet completely, such as beans, pea pods, olives, garbanzo beans, fava beans, lentils, and pickles. These foods have certain properties which could potentially trigger migraine headaches in certain people, especially those who are already prone to getting them from time to time.